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A174790 Triangle read by rows: T(n,m) = 1 + ((-1 + binomial(n, m))*(n!)^2)/(m!*(n - m)!). 2
1, 1, 1, 1, 5, 1, 1, 37, 37, 1, 1, 289, 721, 289, 1, 1, 2401, 10801, 10801, 2401, 1, 1, 21601, 151201, 273601, 151201, 21601, 1, 1, 211681, 2116801, 5997601, 5997601, 2116801, 211681, 1, 1, 2257921, 30481921, 124185601, 194745601, 124185601, 30481921, 2257921, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Stefano Spezia, First 101 rows of the triangle, flattened

FORMULA

T(n,m) = ((n!)^2/(m!*(n - m)!))*binomial(n, m) - ((n!)^2/(m!*(n - m)!)) + 1.

From Stefano Spezia, Dec 18 2018: (Start)

T(n,m) = 1 + ((-1 + binomial(n, m))*(n!)^2)/(m!*(-m + n)!).

T(n,m) = 1 + ((-1 + A007318(n, m))*A001044(n)/(A000142(m)*A000142(-m + n)).

(End)

EXAMPLE

n\m | 0         1         2         3         4         5         6         7

----|------------------------------------------------------------------------

  0 | 1

  1 | 1         1

  2 | 1         5         1

  3 | 1        37        37         1

  4 | 1       289       721       289         1

  5 | 1      2401     10801     10801      2401         1

  6 | 1     21601    151201    273601    151201     21601         1

  7 | 1    211681   2116801   5997601   5997601   2116801    211681         1

...

MATHEMATICA

T[n_, m_] := (n!^2/(m!(n - m)!))*Binomial[n, m] - (n!^2/(m!(n - m)!)) + 1; Flatten[Table[Table[T[n, m], {m, 0, n}], {n, 0, 10}]]

PROG

(GAP) Flat(List([0..10], n->List([0..n], m->1 + ((- 1 + Binomial(n, m))*(Factorial(n)^2)/(Factorial(m)*Factorial(-m+n))))

)); # Stefano Spezia, Dec 18 2018

(PARI)

T(n, m)= 1 + ((- 1 + binomial(n, m))*(n!)^2)/(m!*(-m+n)!);

tabl(nn) = for(n=0, nn, for(m=0, n, print1(T(n, m), ", ")); print);

tabl(10) \\ Stefano Spezia, Dec 18 2018

CROSSREFS

Cf. A007318, A001044, A000142.

Cf. A320329 (row sums).

Sequence in context: A058720 A015116 A322220 * A156691 A246051 A111820

Adjacent sequences:  A174787 A174788 A174789 * A174791 A174792 A174793

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, Mar 29 2010

EXTENSIONS

Edited by Stefano Spezia, Dec 18 2018

STATUS

approved

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Last modified April 20 14:27 EDT 2019. Contains 322310 sequences. (Running on oeis4.)